1
|
Nastac ML, Ewart RJ, Sengupta W, Schekochihin AA, Barnes M, Dorland WD. Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence. Phys Rev E 2024; 109:065210. [PMID: 39021007 DOI: 10.1103/physreve.109.065210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2023] [Accepted: 02/02/2024] [Indexed: 07/20/2024]
Abstract
We consider a nearly collisionless plasma consisting of a species of "test particles" in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field-a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space-known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C_{2}∝∫∫dxdv〈f^{2}〉-a quantity that here plays the role of (negative) entropy of the distribution function. We find that C_{2} is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C_{2} in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C_{2} to high s (towards the collisional dissipation range) at every k, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C_{2} is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k-space (s-space) flux of C_{2} is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s) plane, with power-law asymptotics at large k and s. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a "critical balance" in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.
Collapse
Affiliation(s)
- Michael L Nastac
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- St. John's College, Oxford OX1 3JP, United Kingdom
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Robert J Ewart
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- Balliol College, Oxford OX1 3BJ, United Kingdom
| | - Wrick Sengupta
- Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08543, USA
- Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540, USA
| | - Alexander A Schekochihin
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- Merton College, Oxford OX1 4JD, United Kingdom
| | - Michael Barnes
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- University College, Oxford OX1 4BH, United Kingdom
| | - William D Dorland
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20740, USA
| |
Collapse
|
2
|
Zhou M, Liu Z, Loureiro NF. Electron heating in kinetic-Alfvén-wave turbulence. Proc Natl Acad Sci U S A 2023; 120:e2220927120. [PMID: 37252951 PMCID: PMC10265953 DOI: 10.1073/pnas.2220927120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 04/23/2023] [Indexed: 06/01/2023] Open
Abstract
We report analytical and numerical investigations of subion-scale turbulence in low-beta plasmas using a rigorous reduced kinetic model. We show that efficient electron heating occurs and is primarily due to Landau damping of kinetic Alfvén waves, as opposed to Ohmic dissipation. This collisionless damping is facilitated by the local weakening of advective nonlinearities and the ensuing unimpeded phase mixing near intermittent current sheets, where free energy concentrates. The linearly damped energy of electromagnetic fluctuations at each scale explains the steepening of their energy spectrum with respect to a fluid model where such damping is excluded (i.e., a model that imposes an isothermal electron closure). The use of a Hermite polynomial representation to express the velocity-space dependence of the electron distribution function enables us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.
Collapse
Affiliation(s)
- Muni Zhou
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Astrophysical Sciences, Princeton University, Princeton, NJ08544
- School of Natural Science, Institute for Advanced Study, Princeton, NJ08544
| | - Zhuo Liu
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Nuno F. Loureiro
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA02139
| |
Collapse
|
3
|
Verscharen D, Klein KG, Maruca BA. The multi-scale nature of the solar wind. LIVING REVIEWS IN SOLAR PHYSICS 2019; 16:5. [PMID: 31929769 PMCID: PMC6934245 DOI: 10.1007/s41116-019-0021-0] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2019] [Accepted: 11/09/2019] [Indexed: 05/29/2023]
Abstract
The solar wind is a magnetized plasma and as such exhibits collective plasma behavior associated with its characteristic spatial and temporal scales. The characteristic length scales include the size of the heliosphere, the collisional mean free paths of all species, their inertial lengths, their gyration radii, and their Debye lengths. The characteristic timescales include the expansion time, the collision times, and the periods associated with gyration, waves, and oscillations. We review the past and present research into the multi-scale nature of the solar wind based on in-situ spacecraft measurements and plasma theory. We emphasize that couplings of processes across scales are important for the global dynamics and thermodynamics of the solar wind. We describe methods to measure in-situ properties of particles and fields. We then discuss the role of expansion effects, non-equilibrium distribution functions, collisions, waves, turbulence, and kinetic microinstabilities for the multi-scale plasma evolution.
Collapse
Affiliation(s)
- Daniel Verscharen
- Mullard Space Science Laboratory, University College London, Dorking, RH5 6NT UK
- Space Science Center, University of New Hampshire, Durham, NH 03824 USA
| | - Kristopher G. Klein
- Lunar and Planetary Laboratory and Department of Planetary Sciences, University of Arizona, Tucson, AZ 85719 USA
| | - Bennett A. Maruca
- Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 USA
| |
Collapse
|
4
|
Kawazura Y, Barnes M, Schekochihin AA. Thermal disequilibration of ions and electrons by collisionless plasma turbulence. Proc Natl Acad Sci U S A 2019; 116:771-776. [PMID: 30598448 PMCID: PMC6338852 DOI: 10.1073/pnas.1812491116] [Citation(s) in RCA: 66] [Impact Index Per Article: 13.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/04/2022] Open
Abstract
Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, turbulent plasma? And, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion disks around black holes. In the context of disks, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: Collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, [Formula: see text]: It ranges from [Formula: see text] at [Formula: see text] to at least 30 for [Formula: see text] This energy partition is approximately insensitive to the ion-to-electron temperature ratio [Formula: see text] Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high [Formula: see text] and hotter electrons at low [Formula: see text] Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high [Formula: see text] and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when [Formula: see text] and by linear phase mixing (Landau damping) when [Formula: see text].
Collapse
Affiliation(s)
- Yohei Kawazura
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom;
| | - Michael Barnes
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Culham Centre for Fusion Energy, Culham Science Centre, Abingdon OX14 3DB, United Kingdom
| | - Alexander A Schekochihin
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Merton College, Oxford OX1 4JD, United Kingdom
| |
Collapse
|
5
|
Camporeale E, Sorriso-Valvo L, Califano F, Retinò A. Coherent Structures and Spectral Energy Transfer in Turbulent Plasma: A Space-Filter Approach. PHYSICAL REVIEW LETTERS 2018; 120:125101. [PMID: 29694094 DOI: 10.1103/physrevlett.120.125101] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2017] [Revised: 02/15/2018] [Indexed: 06/08/2023]
Abstract
Plasma turbulence at scales of the order of the ion inertial length is mediated by several mechanisms, including linear wave damping, magnetic reconnection, the formation and dissipation of thin current sheets, and stochastic heating. It is now understood that the presence of localized coherent structures enhances the dissipation channels and the kinetic features of the plasma. However, no formal way of quantifying the relationship between scale-to-scale energy transfer and the presence of spatial structures has been presented so far. In the Letter we quantify such a relationship analyzing the results of a two-dimensional high-resolution Hall magnetohydrodynamic simulation. In particular, we employ the technique of space filtering to derive a spectral energy flux term which defines, in any point of the computational domain, the signed flux of spectral energy across a given wave number. The characterization of coherent structures is performed by means of a traditional two-dimensional wavelet transformation. By studying the correlation between the spectral energy flux and the wavelet amplitude, we demonstrate the strong relationship between scale-to-scale transfer and coherent structures. Furthermore, by conditioning one quantity with respect to the other, we are able for the first time to quantify the inhomogeneity of the turbulence cascade induced by topological structures in the magnetic field. Taking into account the low space-filling factor of coherent structures (i.e., they cover a small portion of space), it emerges that 80% of the spectral energy transfer (both in the direct and inverse cascade directions) is localized in about 50% of space, and 50% of the energy transfer is localized in only 25% of space.
Collapse
Affiliation(s)
- E Camporeale
- Center for Mathematics and Computer Science (CWI), Amsterdam 1098 XG, The Netherlands
| | - L Sorriso-Valvo
- CNR-Nanotec-Unità di Cosenza, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - F Califano
- Dipartimento di Fisica "E. Fermi," Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
| | - A Retinò
- Centre National de la Recherche Scientifique, LPP UMR 7648, Ecole Polytechnique, Universit Pierre et Marie Curie Paris VI, Observatoire de Paris, Route de Saclay Palaiseau 91128, France
| |
Collapse
|
6
|
|
7
|
Grošelj D, Mallet A, Loureiro NF, Jenko F. Fully Kinetic Simulation of 3D Kinetic Alfvén Turbulence. PHYSICAL REVIEW LETTERS 2018; 120:105101. [PMID: 29570310 DOI: 10.1103/physrevlett.120.105101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Revised: 01/25/2018] [Indexed: 06/08/2023]
Abstract
We present results from a three-dimensional particle-in-cell simulation of plasma turbulence, resembling the plasma conditions found at kinetic scales of the solar wind. The spectral properties of the turbulence in the subion range are consistent with theoretical expectations for kinetic Alfvén waves. Furthermore, we calculate the local anisotropy, defined by the relation k_{∥}(k_{⊥}), where k_{∥} is a characteristic wave number along the local mean magnetic field at perpendicular scale l_{⊥}∼1/k_{⊥}. The subion range anisotropy is scale dependent with k_{∥}<k_{⊥} and the ratio of linear to nonlinear time scales is of order unity, suggesting that the kinetic cascade is close to a state of critical balance. Our results compare favorably against a number of in situ solar wind observations and demonstrate-from first principles-the feasibility of plasma turbulence models based on a critically balanced cascade of kinetic Alfvén waves.
Collapse
Affiliation(s)
- Daniel Grošelj
- Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, D-85748 Garching, Germany
| | - Alfred Mallet
- Space Science Center, University of New Hampshire, Durham, New Hampshire 03824, USA
| | - Nuno F Loureiro
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Frank Jenko
- Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, D-85748 Garching, Germany
| |
Collapse
|